Table Of ContentMon.Not.R.Astron.Soc.000,1–13(2012) Printed15January2013 (MNLATEXstylefilev2.2)
Physical properties of the WASP-44 planetary system from
simultaneous multi-colour photometry
3 L. Mancini,1⋆ N. Nikolov,1 J. Southworth,2 G. Chen,1,3 J. J. Fortney,4
1
0 J. Tregloan-Reed,2 S. Ciceri,1 R. van Boekel,1 and Th. Henning1
2 1Max Planck Institute for Astronomy, K¨onigstuhl 17, 69117 – Heidelberg, Germany
n 2Astrophysics Group, Keele University,Newcastle-under-Lyme, ST5 5BG, UK
a 3Purple Mountain Observatory & Key Laboratory for Radio Astronomy, 2 West Beijing Road, Nanjing 210008, China
J 4Department of Astronomy & Astrophysics, Universityof California, Santa Cruz, CA 95064, USA
4
1
Accepted. Received.
]
P
E
ABSTRACT
.
h We present ground-based broad-band photometry of two transits in the WASP-44
p planetary system obtained simultaneously through four optical (Sloan g′, r′, i′, z′)
- andthree near-infrared(NIR; J, H, K)filters.We achievedlowscatters of1–2mmag
o per observationinthe optical bands with a cadence of ≈48s,but the NIR-band light
r
t curves present much greater scatter. We also observed another transit of WASP-44
s
b by using a Gunn-r filter and telescope defocussing, with a scatter of 0.37 mmag
a
[ per point and an observing cadence around 135s. We used these data to improve
measurementsofthe time ofmid-transitandthe physicalpropertiesof the system.In
1
particular,weimprovedtheradiusmeasurementsofthestarandplanetbyfactorsof3
v and4,respectively.WefindthattheradiusofWASP-44bis1.002±0.033±0.018R
5 Jup
(statistical and systematic errors, respectively), which is slightly smaller than previ-
0
ously thought and differs from that expected for a core-free planet. In addition, with
0
3 the helpofa syntheticspectrum, weinvestigatedthe theoretically-predictedvariation
. of the planetary radius as a function of wavelength, covering the range 370–2440nm.
1
We can rule out extreme variations at optical wavelengths, but unfortunately our
0
dataarenotpreciseenough(especiallyinthe NIRbands)todifferentiatebetweenthe
3
theoretical spectrum and a radius which does not change with wavelength.
1
:
v Key words: stars: planetary systems – stars: fundamental parameters – stars: indi-
i vidual: WASP-44
X
r
a
1 INTRODUCTION 2012; Bakos et al. 2012; Hartman et al. 2012; Penev et al.
2013; Bryan et al. 2012; Beatty et al. 2012; Siverd et al.
The transit method is not only an excellent technique to
2012) are close-in hot Jupiters, because thedetection prob-
detectextrasolar planets, butalso provideunrivalledaccess
ability for such planets is much greater than for those
to their physical parameters. The geometry of a transiting
which are smaller or on wider orbits. Hot Jupiters are also
extrasolar planet (TEP) system permits measurement of
relatively straightforward to detect via the radial velocity
the mass, radius and density of a planet. These quantities
method, as they induce comparatively large velocity vari-
requiresomeinputfromstellarevolutionarytheory,butthe
ations in their host stars. The existence of hot Jupiters
planetary surface gravity can be measured directly. A TEP
was unexpected (Mayor and Queloz 1995), and led to the
system is therefore a potential horn of plenty of physical
birth of new formation and migration theories (see the re-
information on planetary systems (Seager & Sasselov 2000;
views of D’Angelo et al. 2010 and Lubow and Ida 2010).
Sudarskyet al. 2000; Brown et al. 2001; Hubbardet al.
Thebias of theground-based surveysin favour of thisclass
2001; Seager & Mall´en-Ornelas 2003; Sudarsky et al.
of planets is clear, whereas the Kepler satellite has already
2003; Charbonneau et al. 2005; Holman & Murray 2005;
found hundreds of smaller and longer-period planet candi-
Winn et al. 2005; Southworth et al. 2007).
dates from only 16 months of data (Borucki et al. 2011a,b;
Currently, most of the TEPs discovered by ground-
Batalha et al. 2012).
basedtransitsurveys(e.g.Hellier et al.2012;Smalley et al.
AnotherfascinatingopportunityofferedbyTEPsisthe
possibility to probe their atmospheres. Due to atomic and
⋆ [email protected] molecular absorption, the analysis of the spectrum of the
2 L. Mancini et al.
parent stars during transit (primary eclipse) is an excellent wavelength shift in absorption lines from carbon monoxide
way to probe their atmospheric composition. The existence in the planet’s atmosphere (Snellen et al. 2010).
oftwodifferentclassesofhotJupiters(pMandpL)hasbeen High-resolutionNIRspectroscopicmeasurementsatthe
suggestedaccordingtotheincidentstellarfluxreceivedfrom Keck telescopes over the wavelength range 2100–2400nm,
the parent star and to the expected amount of absorbing revealedanupperlimitforCOabsorptionintheatmosphere
substances,suchasgaseoustitaniumoxide(TiO)andvana- of HD209458b (Deming et al. 2005), and that the super-
diumoxide(VO),intheiratmospheres(Fortneyet al.2008). Earth GJ1214b is a H-dominated planet (Crossfield et al.
Accordingtotheoreticalmodels,thesetwooxidizedelements 2011).GJ1214bwasalsostudiedthroughmulti-objectspec-
should be extremely strong absorbers for the pM class be- troscopy from 0.61 to 0.85 µm, and in the J, H, and
tween450nmand700nm,causingsuchplanetstohaveahot K atmospheric windows by using VLT/FORS and Magel-
(∼2000 K) stratosphere. An observable variation of radius lan/MMIRS, the data being consistent with a featureless
with wavelength, due to the opacities of these elements, is transmission spectrum for theplanet (Bean et al. 2011).
consequently expected in the optical bands (Burrows et al. A radius variation with wavelength was investigated
2007). The radius of a pM planet should be 3% lower at for HD209458b by Knutsonet al. (2007a) using ten-colour
350–400nmversus500–700nm.Theradiusvariationsforthe HSTphotometry.Differentanalysesofthesedatahavegiven
colderpL-classplanets(incidentflux<109ergs−1cm−2)are conflicting results (Knutsonet al. 2007a; Barman 2007;
smaller, but a significant contribution to the opacity in the Singet al. 2008a; Southworth 2008). An HST transmis-
optical band is expected from NaI at ∼590nm, and KI at sion spectrum of HD189733b covering 270–570nm showed
∼770nm (Fortney et al. 2008, 2010; Burrows et al. 2010). a gradual increase of radius towards shorter wavelengths
Transmission spectroscopy is essential for detecting atmo- whichwasinterpretedasaresultofRayleighscatteringfrom
spheric absorbers, and is complementary to observations at ahigh-altitudeatmospherichaze(Singet al.2011a).Butob-
secondary eclipse which can help to determine the day-side servationscovering550–1050nmdidnotprovideanyindica-
atmospheric temperature structure. tion of the expected NaI or KI features (Pont et al. 2008),
Accurate measurements of planet radii provide critical andthoseintheranges1082–1168nmand1514–1693nmdid
constraints for astrophysicists working on planet formation not detect any variation in planetary radius (Gibson et al.
and evolution, because they provide an indication of the 2012a).
planet internal heat, structure and composition, as well as UsingtheGranTelescopioCanarias (GTC),Sing et al.
theheatingmechanismforthosewhichundergostrongtidal (2011b)claimedthefirstevidenceforpotassiuminanextra-
effects and stellar irradiation, allowing the discrimination solar planet, from photometry of the XO-2 system in four
betweencompetingtheories(Pollack et al.1996;Boss1997). narrow red-optical passbands, by detecting KI absorption
In particular, the most irradiated hot Jupiters are charac- at 766.5nm. This technique was also used by Col´on et al.
terised by anomalously inflated radii for which the expla- (2012)tostudyHD80606b,whofoundanunexplainedlarge
nation remains unclear (Bodenheimer et al. 2003; Gu et al. (≈ 4.2%) change in the apparent planetary radius between
2004; Gaudi 2005; Fortney et al. 2007; Jackson et al. the wavelengths 769.9 and 777.4nm. The differential spec-
2008; Dobbs-Dixon & Lin 2008; Batygin et al. 2009; trophotometrytechniquewasusedtoobtaintwotransitlight
Ibgui& Burrows 2009; Miller et al. 2009; Ibgui et al. curves of XO-2b with GTC by Sing et al. (2012), who de-
2010; Laughlin et al. 2011; Miller & Fortney 2011; tected significant absorption in the planetary atmosphere
Demory & Seager 2011). in a 50-˚A bandpass centred on the NaI doublet. Instead,
Photometric and spectroscopic analyses of planet at- the presence of an Na-rich atmosphere in WASP-29b was
mospheres started with the use of optical, near-infrared recently ruled out by Gibson et al. (2012b), using Gemini-
(NIR) and infrared (IR) instruments aboard the Hub- South GMOS transit spectrophotometry.
ble and Spitzer space telescopes (Charbonneau et al. 2002; Southworth et al. (2012b) recently presented a study
Vidal-Madjar et al. 2003, 2004; Richardson et al 2006; of possible radius variations of the hot Jupiter HAT-P-5b,
Tinetti et al.2007;Knutson et al.2007a,b;Richardson et al based on photometry obtained simultaneous in the u, g, r
2007; Swain et al. 2008; Pont et al. 2008; Beaulieu et al. andI passbands.Theauthorsdetectedagradualincreaseof
2008,2010,2011;Gillon et al.2012)andledtothedetection theradiusbetween450nmand850nm,plusasubstantially
ofRayleighscatteringinafewhotJupiteratmospheres,plus larger planetary radius at 350nm. The latter phenomenon
absorptionlinesassociatedwithH2O,Na,CH4,TiOandVO can be explained by systematic errors in the u-band pho-
(seeabovereferences butalsoBallester et al.2007;Barman tometry, but is also consistent with Rayleigh scattering as
2007; Sing et al. 2008a,b; Lecavelier des Etangs et al. 2008; in the case of HD189733b. A similar multi-band investiga-
D´esert et al. 2008; Zahnleet al. 2009; Spiegel et al. 2009; tionofHAT-P-8(Mancini et al.2013)suggeststhepresence
Fossati et al. 2010; Tinetti et al. 2010; D´esert et al. 2011; ofstrongopticalabsorbersneartheterminatorofthisTEP.
Wood et al. 2011;Gibson et al.2011;Crossfield et al. 2012; Here we focus our attention on the planetary system
Crouzet et al. 2012). WASP-44,discoveredbyAnderson et al.(2012).Thesystem
After a number of pioneering experiments with null consistsofa0.89MJup planetona2.42-dayorbitaroundan
results, ground-based spectroscopy also obtained some in- inactiveG8Vstar(V =12.9,[Fe/H]=+0.06).Inthiswork
teresting results. Observations performed at the Hobby- wepresentthefirstphotometricfollow-upsinceitsdiscovery
Eberly and Subaru telescopes, in the spectral range 500– was announced, covering seven optical/NIR passbands. We
900nm, detected Na absorption in the transmission spec- refine the physical properties of the system and attempt to
trumofHD189733b(Redfieldet al.2008)andHD209458b probefor radius variations in these passbands.
(Snellen et al. 2008). NIR spectroscopy of HD209458b at Our paper is structured as follows. In § 2 we describe
the VLT in the range 2291–2349nm reported a significant the instruments used for the observations and give some
Physical properties of WASP-44b 3
details concerning the data reduction. In § 3 we illustrate
Table 2. Excerpts of the light curves of WASP-44. The full
the analysis of the data which led to the refinement of the datasetwillbemadeavailableattheCDS.
orbital period and the physical properties of the WASP-44
system. Then, we examine the variation of the planetary Telescope Filter BJD(TDB) Diff.mag. Error
radius with wavelength. Finally, in § 4 we summarise our
INT Gunnr 2455807.576418 0.00036 0.00041
results.
INT Gunnr 2455807.579370 0.00009 0.00042
ESO2.2m Sloang′ 2455836.647443 0.00126 0.00100
ESO2.2m Sloang′ 2455836.649992 0.00210 0.00123
2 OBSERVATIONS AND DATA REDUCTION ESO2.2m Sloanr′ 2455836.647443 -0.00097 0.00088
ESO2.2m Sloanr′ 2455836.649992 0.00079 0.00109
Two transits of WASP-44b were recorded on 2011 October
ESO2.2m Sloani′ 2455836.647443 0.00096 0.00109
2 and 6, using the Gamma Ray Burst Optical and Near-
ESO2.2m Sloani′ 2455836.649992 0.00138 0.00134
Infrared Detector (GROND) instrument mounted on the
MPG1/ESO2.2mtelescopeatESOLaSilla,Chile.GROND ESO2.2m Sloanz′ 2455836.647443 -0.00143 0.00142
ESO2.2m Sloanz′ 2455836.649992 0.00100 0.00179
is an imaging system capable of simultaneous photometric
observations in four optical (identical to Sloan g′, r′, i′, z′)
and three NIR (J, H,K) passbands (Greiner et al. 2008).
flats,andusedthemtocorrectthescienceimages.Aperture
Each of the four optical channels is equipped with a back-
photometry was performed using the idl2/astrolib3 im-
illuminated 2048 × 2048 E2V CCD, with a field of view
plementation of daophot (Stetson 1987; Southworth et al.
(FOV) of 5.4′ ×5.4′ at a scale of 0.158′′/pixel. The three
2009). The apertures were placed manually and shifted to
NIR channels use 1024×1024 Rockwell HAWAII-1 arrays
account for pointing variations, which were measured by
with a FOV of 10′×10′ at 0.6′′/pixel.
cross-correlating each image against a reference image. We
We applied a slight telescope defocus and obtained
experimentedwithwiderangeofaperturesizesandretained
repeated integrations during both runs. Autoguiding was
those which gave photometry with the lowest scatter com-
used to keep the stars on the same pixels. All images were
paredtoafittedmodel. Thetimes ofobservation werecon-
digitised using the fast read-out mode (∼10s) to improve
verted from UTC to BJD(TDB) using the IDL procedures
the time sampling. On 2011/10/02 we monitored the flux
of Eastman et al. (2010).
of WASP-44 in nearly photometric conditions, and saw a
Differentialphotometrywasobtainedineachfilterusing
monotonical seeing decline from 0.50′′ to 1.03′′ as airmass
between two and four comparison stars, two of which were
decreased from 1.08 to 1.05 and then rose to 1.54. Expo-
enough bright to produce count rates comparable to those
sures of 20s were used in the optical channels and stacks
ofWASP-44.Allgoodcomparisonstarswerecombinedinto
of four 4s images were obtained in the NIR channels. On
one ensemble by weighted flux summation. Slow variations
2011/10/06 we experienced worse atmospheric conditions,
in the apparent brightness of the reference stars, primarily
andtheairmasschangedfrom2.07to1.05duringourobser-
attributable to atmospheric effects, were treated by fitting
vations.Imageswithexposuretimesof25swereobtainedin
a polynomial to regions outside transit, whilst simultane-
theopticalchannels,andstacksofsix4simagesintheNIR
ouslyoptimisingtheweightsofthecomparison stars.Given
channels. For theoptical frames we selected a fast read-out
the limited number of comparison stars in the small field
mode, which provided a 15s readout. Due to the necessary
of view of GROND, and the shape of the slow brightness
synchronization of the optical and NIR starting times for
variations, we used a second-order polynomial versus time.
eachexposure,theobservingcadenceresultedtobeof≈48
Uncertaintiesintroduced bythis procedurewere considered
and ≈25s in the optical and NIRbandsrespectively.
inthemodellingofthelightcurves,asdescribedinthenext
Another full transit of WASP-44b was observed
section.
throughaGunnrfilteronthenightof2011/09/02usingthe
TheNIRframeswerealsocalibratedinastandardway,
WideFieldCamera(WFC)onthe2.5mIsaacNewtonTele-
including dark subtraction, flat correction and sky subtrac-
scope(INT)atLaPalma.WFCisanopticalmosaiccamera
tion. The master sky images used in sky subtraction were
consisting of four thinned EEV 2k×4k CCDs, with a plate
created from two sets of 20-position dithering sky measure-
scale of0.33′′pixel−1.Thetelescope washeavilydefocussed
ments,onebeforethescienceobservationandoneafter.We
so the point spread function (PSF) of the target and com-
performed aperture photometry on the calibrated NIR im-
parisonstarshadnotmorethan35000countsperpixel.We
ages as well. The aperture locations were determined us-
usedthefast readoutmodetoreducereadouttimedownto
ingidl/find.Variouscombinationsofapertureandannulus
about 15s. An exposure time of 2min per frame was used,
sizes were check to find the best photometry. We also care-
and the resulting observing cadence was roughly 135s. The
fully made ensembles of comparison stars, and chose the
night was photometric. We were not able to autoguide the
groupwhichshowedtheleastdeviationfromthetarget.Af-
telescope as the autoguider is incorporated into the WFC
ter normalising the target light curve with the composite
andsowasalsodefocussed.Asummaryoftheobservational
reference light curve, we decorrelated the data with posi-
data is reported in Table1.
tion, seeing and airmass in order to remove the correlated
Reduction of the optical frames was undertaken using
standard methods. We created master bias and flat-field
images by median-combining sets of bias images and sky 2 The acronym idl stands for Interactive Data Language and
isa trademark of ITT Visual Information Solutions. For further
detailsseehttp://www.ittvis.com/ProductServices/IDL.aspx.
1 MaxPlanckGesellschaft. 3 http://idlastro.gsfc.nasa.gov/
4 L. Mancini et al.
Table1.Logoftheobservationspresentedinthiswork.Nobsisthenumberofobservationsand“Moonillum.”isthefractionalillumination
oftheMoonatthemidpointofthetransit.Theaperturesizesaretheradiiofthesoftwareaperturesforthestar,innerskyandoutersky,
respectively. β is the factor used to inflate the errorbars (see § 3). Transit #1 was observed using the 2.5 m INT in La Palma, whereas
transits#2and#3usingtheMPG/ESO2.2mtelescopeinLaSilla.
Transit Date Start/endTime Nobs Exposure Filter Airmass Moon Aperture Scatter β
(UT) time(s) illum. sizes(px) (mmag)
1 20110903 00:28-00:57 156 120 Gunnr 1.60→1.32→2.18 31% 25,35,50 0.37 1.15
2 20111002 03:21-07:35 317 20 Sloang′ 1.08→1.05→1.54 40% 16,35,55 1.23 1.07
2 20111002 03:21-07:35 317 20 Sloanr′ 1.08→1.05→1.54 40% 17,40,60 1.08 1.00
2 20111002 03:21-07:35 317 20 Sloani′ 1.08→1.05→1.54 40% 20,30,45 1.34 1.00
2 20111002 03:21-07:35 317 20 Sloanz′ 1.08→1.05→1.54 40% 12,25,40 1.79 1.10
2 20111002 03:21-07:35 631 3 J 1.08→1.05→1.54 40% 6.0,15.0,23.0 7.66 1.09
2 20111002 03:21-07:35 631 3 H 1.08→1.05→1.54 40% 2.5,11.5,21.0 8.11 1.08
2 20111002 03:21-07:35 631 3 K 1.08→1.05→1.54 40% 3.0,11.0,21.0 5.98 1.15
3 20111006 03:21-07:35 317 25 Sloang′ 2.07→1.05 80% 19,30,50 1.89 1.06
3 20111006 03:21-07:35 313 25 Sloanr′ 2.07→1.05 80% 22,40,60 1.70 1.32
3 20111006 03:21-07:35 313 25 Sloani′ 2.07→1.05 80% 20,40,60 1.79 1.35
3 20111006 03:21-07:35 313 25 Sloanz′ 2.07→1.05 80% 16,40,60 2.52 1.26
3 20111006 03:21-07:35 623 3 J 2.07→1.05 80% 9.0,17.0,25.0 5.23 1.38
3 20111006 03:21-07:35 623 3 H 2.07→1.05 80% 6.5,13.5,22.0 6.96 1.34
3 20111006 03:21-07:35 623 3 K 2.07→1.05 80% 3.5,4.5,18.0 7.65 1.04
rednoise.WeextractedtheoptimalNIRlightcurvesforthe weights by a factor β >1. The β approach (e.g. Pont et al.
two nights according to the rms of O–C residuals and con- 2006; Winn et al. 2007) is a widely used way to assess
sistencyofthetransitdepthbetweentwonights.Detailsare red noise (e.g. Gillon et al. 2006; Winn et al. 2008, 2009;
given in Appendix A. The resulting photometry is given in Gibson et al. 2008; Nikolov et al. 2012; Southworth et al.
Table2. 2012a,b). The factor β is a measurement of how close the
Although we have performed all the possible calibra- data noise is to the Poisson approximation, and is found
tions and corrections, the scatter of the NIR data is much by binning the data and evaluating the ratio between the
largerthanthatoftheopticaldata,andtheNIRlightcurves size of the residuals versus what would be expected if the
areheavilydominatedbyrednoise. Thisproblemisrelated data followed Poisson statistics. We evaluated values of the
to the adopted observing strategy that unfortunately did β factorforeachindividualtransitandforgroupsof10dat-
not allow a good SNRto beobtained4. apoints;theyarereportedinTable1.Foramoreexhaustive
Our analysis also included the dataset presented by discussion about rescaling errorbars, see Andrae(2010).
Anderson et al.(2012),whichwasobtainedthroughaGunn
r filter and using EulerCam mounted on the 1.2m Euler-
Swiss telescope at ESO La Silla. 3.1 Period determination
As a first step, we fitted each light curve individually us-
ing the jktebop code (see §3.2) in order to find the tran-
3 ANALYSIS
sit times. Their uncertainties were estimated from Monte
Carlo simulations. To these we added two timings obtained
We have measured the physical properties of the WASP-44
byAnderson et al.(2012)andfourobtainedbyamateuras-
planetarysystemfollowingthemethodologyoftheHomoge-
neous Studies project (Southworth 2008, 2009, 2010, 2011, tronomers, which are available on the TRESCA5 website
(see Table3). Weexcluded from this analysis ourNIR data
2012).Werefer the readerto those works for a detailed de-
sincetheyaremuchnoisierthantheopticalones.Alltimings
scription of theapproach.
wereplacedonBJD(TDB)timesystem.Theresultingmea-
Since the absolute values of the observational errors
surements of transit midpoints were fitted with a straight
from our pipeline (which come ultimately from the aper
line to obtain a neworbital ephemeris:
subroutine)werefoundtobeunderestimated,weadopt the
satarendduacreddpχra2cotficχe2νof=re1s.cTalhineng,tihnemordfoerrteoacahccdoautnatseftortotigmivee- T0 =BJD(TDB)2455434.37642(37)+2.4238133(23)×(E1)
correlatederrors(i.e.rednoise,whichcansignificantlyaffect
where E is the number of orbital cycles after the refer-
ground-based data) and derive more realistic uncertainties,
ence epoch (the midpoint of the first transit observed by
we inflated the errorbars further by multiplying the data
Anderson et al. 2012)and quantitiesinbracketsdenotethe
uncertainty in the final digit of the preceding number. The
4 Afterthesefirstobservations, wechanged ourobservingstrat- fit has χ2ν = 2.42, so the uncertainties were increased to
egy adopting the defocussing technique for GROND. Thanks to account for this. Despite this large χ2ν, we do not note any
this approach, we can now obtain scatter smaller than 2mmag
per observation in the NIR bands and smaller than 1mmag in
theopticalones,withoutcompromisingthesampling(Nikolovet 5 TheTRansitingExoplanetSandCAndidates(TRESCA)web-
al.,inprep.). sitecanbefoundathttp://var2.astro.cz/EN /tresca/index.php
Physical properties of WASP-44b 5
Table 3. Central transit times of WASP-44 and their residuals INT
versustheephemerisderivedinthiswork.TRESCAreferstothe 1.00 æææ æææææ ææ ææææææææææ ææ
“TRansitingExoplanetSandCAndidates”website. ææ æ
æ æ
æ æ
Centraltransittime Cycle Residual Reference æ æ
0.99 æ
BJD(TDB)–2400000 no. (JD) ææ ææ
555555555555448888350122437499......376944764156663641337585794591±±±±±±000000......000000000000000121441546023053 11115566473308 ---000000......000000000000000313050141547045 AATELLoovhnnmmaiddsneeooswrrzzssPoooFFr.nnk..(ee((T(TTttIRNRRaaEllTEE..SSS((Cr22CC)00AAA11)22)))) sedFlux 00..9978 Eulerææææææææææææææææææææææææææææææææææææææææææ æææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææ
55555555888833336666....77772222999907025908±±±±0000....00000000000023210005 111166666666 ---0000....00000000000033418635 TTTThhhhiiiisssswwwwoooorrrrkkkk((((GGGGRRRROOOONNNNDDDDgriz′′′′)))) Nrmali 0.96 ææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææ
55841.57719±0.00035 168 0.00014 Thiswork(GRONDg′)
55841.57757±0.00046 168 0.00052 Thiswork(GRONDr′) INT
55841.57684±0.00028 168 -0.00021 Thiswork(GRONDi′) 0.95 æææ ææææææææææææææææææææææææææææææææææææææææææææææææææææ ææææææææææ ææ
55841.57769±0.00031 168 0.00064 Thiswork(GRONDz′)
s5y61st2e7m.5a86ti2c4d±ev0i.a0t0i0o4n8from28t6he-0p.r0e0d0i7c8tedSaturaernsTit.(tTimReEsS.CAAp)lot 0.94 Eulerææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææ
-0.04 -0.02 0.00 0.02 0.04
of the residuals around the fit is shown in Fig.1. Since the
OrbitalPhase
numberofknownobservedtransitsofthisplanetisstillvery
low,noconclusionscanbedrawnregardingtheexistenceof
Figure 4. As for Fig.2 but for the r−filter INT and Euler
any third body in thesystem.
(Andersonetal.2012)lightcurvesofWASP-44.
3.2 Light curve modelling bestfitsareshowninFig.2and3fortheGRONDdataand
in Fig.4 for the INT and Euler data. The final photomet-
The light curves were modelled using the jktebop6 code.
ricparametersaretheweighted meanofthevaluesforeach
Theprimaryfittedparameterswerethesumandratioofthe
dataset.Theagreementbetweenlightcurvesisexcellent:the
farnadcttihoneaolrbraitdailiionfctlhineasttiaorna,ni.dTphleanfreatc,triAon+arlbraadnidiokf=threbc/ormA-, χ2ν valueoftheagreementoftheindividualparameterswith
respect to the weighted mean is smaller than 0.75 for all
ipsotnheentosrbaritealdesfiemneidmaasjorrAax=isR, aAn/da RanAdarnbd=RRbba/rae,twhheetrreuae hexacveepftoukn,dwhtheirseswiteuafotiuonndtoabmeocdoemstmlyolnardguerrinχg2νooufr1w.6o4r.kWone
radiiofthetwoobjects.Additionalparametersofthefitin-
theHomogeneous Studiespapers.Table4alsoshowsacom-
cludedthelightleveloutsidetransitandthemidpointofthe
parison with theresults from Anderson et al. (2012),which
transit.Limbdarkening(LD)wasimposedusingaquadratic
are in good agreement with ours but have much larger er-
law and the corresponding coefficients fixed at values theo-
rorbars.
retically predicted using model atmospheres (Claret 2004).
Southworth (2008) performed three different treatments of
the LD coefficients: (i) both coefficients fixed to theoreti- 3.3 Physical properties of the WASP-44 system
cal values; (ii) both coefficients fitted; (iii) the linear LD
FollowingtheapproachdescribedinSouthworth(2009),the
coefficient fitted and the nonlinear one fixed to its theoret-
estimation of the physical properties of the WASP-44 sys-
ically predicted value. While the second treatment is possi-
tem was performed making use of standard formula (e.g.
ble only when the data are of high quality, the use of the
Hilditch 2001). We used the photometric parameters mea-
thirdalternativehasanegligibleimpactonthefinalresults.
sured in §3.2, and thevelocity amplitude,effective temper-
Uncertainties were calculated using both Monte Carlo sim-
ulationsand aresidual-permutation algorithm (Southworth ature,andmetallicity ofthestar(KA =138.8±9.0kms−1,
T = 5410 ± 150K, [Fe/H]= +0.06 ± 10) measured by
2008),andthelargerofthetwovalueswasretainedforeach eff
Anderson et al. (2012). We interpolated within tabulations
output quantity. The orbital eccentricity was fixed to zero
fromtheoreticalstellarmodelstofindthebestagreementbe-
(Anderson et al.2012).Allthedatasetsweresolvedindivid-
tween the observed and model-predicted T , and the mea-
ually. As in the previous section, due to their large scatter eff
(see Table1), we did not use the NIR data for estimating suredrA andcalculated RA/a.This yieldedthebest-fitting
mass, radius, surface gravity and mean density of the star
thephysical properties of theplanetary system.
Representative photometric parameters were obtained (MA, RA, loggA and ρA) and of the planet (Mb, Rb, gb
andρ ).Wealsocalculated theorbitalsemi-majoraxis(a),
foreachdatasetandaregiveninTable4.Thecorresponding b
planetary equilibrium temperature (Teq), Safranov number
(Θ),and the evolutionary age of the star.
6 jktebop is written in FORTRAN77 and the source code is The uncertainties in the input parameters were prop-
availableathttp://www.astro.keele.ac.uk/˜ jkt/ agated into the output physical properties using a pertur-
6 L. Mancini et al.
0.006
Ls 0.004
y ç
da 0.002 ç
Hals 0.000 æ ææææææææ ç
u -0.002
d
si -0.004 ç
e
R
-0.006
0 50 100 150 200 250
Cyclenumber
Figure 1.O-Cdiagramofthemid-transittimesofWASP-44bversusalinearephemeris.Thetimingsinblackarefromthiswork,and
ingreyarefromAndersonetal.(2012).Thetimingsobtainedbyamateurastronomersareplottedusingopencircles.Theuncertainties
ofourpointshavebeenrescaled(seetext).
g¢ 0.47Μm g¢ 0.47Μm
1.00 1.00
r¢ 0.62Μm r¢ 0.62Μm
i¢ 0.77Μm i¢ 0.77Μm
0.95 0.95
z¢ 0.93Μm z¢ 0.93Μm
ã
NormalisedFlux 000...889050 HKJ é¨é¨é¨é¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãéããé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãéãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãããé¨ãé¨é¨é¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨éã¨ãéã¨éã¨éã¨é¨éã¨éã¨éã¨éã¨éã¨éã¨éã¨éã¨éã¨éã¨éã¨éã¨éã¨éã¨éã¨éã¨éã¨éã¨éã¨éã¨éã¨éã¨éã¨éãé¨ã¨éãé¨ã¨éãé¨ã¨éãé¨ã¨éãé¨ã¨éãé¨ã¨éãé¨ã¨éãé¨ã¨éãé¨ã¨éãé¨ã¨éãé¨ã¨éã¨ã¨éãé¨ã¨éãé¨ã¨éãé¨ã¨éã騨éé¨ã¨éãé¨ã¨éãé¨ã¨éãé¨ã¨éãé¨ã¨éãé¨ã¨éãé¨ã¨éãé¨ã¨éãé¨ã¨éãé¨ã¨éãé¨ã¨éãé¨ã¨éãé¨ã¨éãé㨨éãéã¨é¨ãé㨨ãã¨éãéã¨é¨é¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãã¨é¨ãéã¨é¨ãéã¨é¨ãã¨éãéã¨é¨ãé¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãé㨨ãé¨é¨ãéã¨é¨ãéã¨é¨ãéãé¨ãéã¨é¨éã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨éã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãé㨨ãéãé¨ãéã¨é¨é㨨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãã¨éãéã¨é¨ãé¨é¨ãé㨨ãã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ã㨨ãã¨é¨ãéã¨éãéãé¨ãéã¨é¨ã¨ã¨éã¨éã¨éã¨éã¨éã¨éã¨éã¨éã¨ã¨éã¨éã¨éã¨éã¨éã¨éã¨éã¨éã¨éã¨éã¨ã¨ããã112...262460ΜΜΜmmm 000...889050 HKJ é¨é¨é¨é¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãéããé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãéãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãããé¨ãé¨é¨é¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨éã¨éã¨ãéã¨éã¨éã¨é¨éã¨éã¨éã¨éã¨éã¨éã¨éã¨éã¨éã¨éã¨éã¨éã¨éã¨éã¨éã¨éã¨éã¨éã¨éã¨éã¨éã¨éã¨éã¨éãé¨ã¨éãé¨ã¨éãé¨ã¨éãé¨ã¨éã騨éãé¨ã¨éãé¨ã¨éãé¨ã¨éãé¨ã¨éãé¨ã¨éãé¨ã¨éã¨ã¨éãé¨ã¨éãé¨ã¨éãé¨ã¨éã騨éé¨ã¨éãé¨ã¨éãé¨ã¨éãé¨ã¨éãé¨ã¨éãé¨ã¨éãé¨ã¨éãé¨ã¨éãé¨ã¨éãé¨ã¨éãé¨ã¨éãé¨ã¨éãé¨ã¨éãé㨨éãéã¨é¨ãé㨨ãã¨éãéã¨é¨é¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãã¨é¨ãéã¨é¨ãéã¨é¨ãã¨éãéã¨é¨ãé¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãé㨨ãé¨é¨ãéã¨é¨ãéã¨é¨ãéãé¨ãéã¨é¨éã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨éã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãé㨨ãéãé¨ãéã¨é¨é㨨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãã¨éãéã¨é¨ãé¨é¨ãé㨨ãã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ã㨨ãã¨é¨ãéã¨éãéãé¨ãéã¨é¨ã¨ã¨éã¨éã¨éã¨éã¨éã¨éã¨éã¨éã¨ã¨éã¨éã¨éã¨éã¨éã¨éã¨éã¨éã¨éã¨éã¨ã¨ããã112...262460ΜΜΜmmm
-0.04 -0.02 0.00 0.02 0.04 -0.04 -0.02 0.00 0.02 0.04
OrbitalPhase OrbitalPhase
Figure 2.Firstset(2011/10/02) ofGROND lightcurves of WASP-44comparedto thebest jktebopfits usingthe quadraticLD law.
Theresidualsofthefitsareplottedatthebaseofthefigure,offsetfromzero.
bation analysis (Southworth et al. 2005). Systematic errors agreement with our own. In particular, we improved the
were assessed by comparing results from five different sets measurement precisions of the radii of both the planet and
of theoretical models (see Southworth 2010). The sets of theparentstar,byfactorsof4and3respectively.Theradius
physical properties found using each set of stellar models ofWASP-44bthatwefound(1.002±0.033±0.018RJup)is
is shown in Table5 and the final physical properties of the smallerthanthatmeasuredinthediscoverypaperanddoes
WASP-44system aregiven inTable6.Theresultsobtained not match the predicted radii of coreless hot-Jupiter plan-
by Anderson et al. (2012) are less precise but are in good etsasestimatedbyFortney et al.(2007).Accordingtotheir
Physical properties of WASP-44b 7
g¢ 0.47Μm g¢ 0.47Μm
1.00 1.00
r¢ 0.62Μm r¢ 0.62Μm
i¢ 0.77Μm i¢ 0.77Μm
0.95 0.95
z¢ z¢
0.93Μm 0.93Μm
ã
NormalisedFlux 000...889050 HKJ ¨¨¨éé¨é¨é¨ãé¨é¨éã¨é¨ãéãéãé¨é¨ãéãéãéãéé¨ãé¨ãé¨ãé¨ãé¨ãé¨é¨é¨ãé¨ãé¨ãé¨ãé¨ãéãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨é¨ãé¨ãé¨ãé¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãé¨ãé¨ãéãé¨ãé¨ãé¨ãéã¨é¨ãé¨ãé¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéãéãéãéãéãéã¨éã¨éã¨éã¨éã¨éã¨é¨é¨é¨é¨é¨é¨ã㨨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãéã¨é¨ãé¨ãé¨ãéã¨é¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãé¨é¨ãéã¨é¨ãé¨ãé¨ãé¨ãé¨ãéã¨é¨ãéã¨é¨ãé¨ãé¨ãé¨ãé¨ãéã¨é¨ãé¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãé¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨éãéã¨é¨ãé¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéãéãéãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨é¨é¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨éãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéãé¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨éã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãé㨨ãã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ã㨨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãé㨨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãé㨨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãé¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãé㨨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéãéãéãéãéãéãããããã112...262460ΜΜΜmmm 000...889050 HKJ ¨¨¨éé¨é¨é¨ãé¨é¨éã¨é¨ãéãéãé¨é¨ãéãéãéãéé¨ãé¨ãé¨ãé¨ãé¨ãé¨é¨é¨ãé¨ãé¨ãé¨ãé¨ãéãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãéã¨é¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨é¨ãé¨ãé¨ãé¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãé¨ãé¨ãéãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéãéãéãéãéãéã¨éã¨éã¨éã¨éã¨éã¨é¨é¨é¨é¨é¨é¨ã¨ã¨ãé¨ãé¨ãéã¨é¨ãé¨ãé¨ãéã¨é¨ãé¨ãé¨ãéã¨é¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãé¨é¨ãéã¨é¨ãéã¨é¨ãé¨ãé¨ãé¨ãé¨ãéã¨é¨ãé¨ãé¨ãé¨ãé¨ãéã¨é¨ãé¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨éã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãé¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨éãéã¨é¨ãé¨é¨ãé¨ãé¨ãéã¨é¨ãéã¨é¨ãéãéãéãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨ãé¨é¨é¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨éãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéãé¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨éã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãé㨨ãã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ã㨨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãé㨨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãé㨨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãé¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãé㨨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéã¨é¨ãéãéãéãéãéãéãããããã112...262460ΜΜΜmmm
-0.04 -0.02 0.00 0.02 0.04 -0.04 -0.02 0.00 0.02 0.04
OrbitalPhase OrbitalPhase
Figure3.Secondset(2011/10/06)ofGRONDlightcurvesofWASP-44comparedtothebestjktebopfitsusingthequadraticLDlaw.
Theresidualsofthefitsareplottedatthebaseofthefigure,offsetfromzero.
Table 4. Parameters of the fits to the ten light curves of WASP-44. The final parameters are the weighted mean of the result for the
GROND,INTandEulerlightcurves.
Source rA+rb k i◦ rA rb
GRONDg′−band#1 0.1368±0.0056 0.1228±0.0023 86.2±0.5 0.1218±0.0020 0.01496±0.00086
GRONDg′−band#2 0.139±0.010 0.1188±0.0028 86.2±1.0 0.1240±0.0090 0.0147±0.0014
GRONDr′−band#1 0.1268±0.0045 0.1175±0.0014 87.3±0.6 0.1135±0.0039 0.01333±0.00060
GRONDr′−band#2 0.1284±0.0080 0.1190±0.0029 86.9±0.8 0.1147±0.0068 0.0136±0.0011
GRONDi′−band#1 0.1363±0.0051 0.1205±0.0016 86.3±0.5 0.1216±0.0044 0.0147±0.00068
GRONDi′−band#2 0.1303±0.0087 0.1204±0.0029 86.7±0.9 0.1163±0.0076 0.0140±0.0011
GRONDz′−band#1 0.1306±0.0075 0.1153±0.0023 86.8±0.8 0.1171±0.0065 0.01349±0.00095
GRONDz′−band#2 0.123±0.010 0.1134±0.0034 87.4±1.5 0.1102±0.0089 0.0125±0.0013
INTr−band 0.1285±0.0029 0.1196±0.0013 86.6±0.3 0.1148±0.0026 0.01373±0.00042
Eulerr−band 0.141±0.011 0.1197±0.0039 85.9±1.0 0.1261±0.0100 0.0151±0.0016
Finalresults 86.59±0.18 0.1168±0.0016 0.0139±0.0002
Andersonetal.(2012) 0.1398 0.1260±0.0030 86.02+−10..1816 0.1242±0.0102 0.0157
8 L. Mancini et al.
Table 5.Derived physical properties of WASP-44 fromusingeach offive different theoretical stellarmodels. In each case gb =21.5±
1.6ms−2,ρA=1.414±0.058ρ⊙ andTeq=1304±37K.
Thiswork Thiswork Thiswork Thiswork Thiswork
(Claretmodels) (Y2 models) (Teramomodels) (VRSSmodels) (DSEPmodels)
Kb (kms−1) 156.1±4.1 151.7±1.0 152.6±4.2 152.7±4.1 153.7±3.2
MA (M⊙) 0.968±0.077 0.888±0.018 0.904±0.074 0.907±0.073 0.924±0.058
RA (R⊙) 0.881±0.025 0.856±0.016 0.862±0.024 0.862±0.024 0.865±0.020
loggA (cgs) 4.534±0.018 4.521±0.010 4.524±0.018 4.524±0.018 4.530±0.016
Mb (Mjup) 0.901±0.075 0.851±0.056 0.861±0.073 0.863±0.073 0.874±0.067
Rb (Rjup) 1.020±0.033 0.992±0.019 0.997±0.033 0.998±0.032 0.994±0.027
ρb (ρjup) 0.793±0.070 0.816±0.069 0.812±0.072 0.811±0.072 0.831±0.071
Θ 0.0640±0.0046 0.0658±0.0045 0.0654±0.0048 0.0654±0.0047 0.0656±0.0046
a(AU) 0.03508±0.00093 0.03409±0.00023 0.03429±0.00093 0.03432±0.00092 0.03454±0.00072
Table 6.FinalphysicalpropertiesoftheWASP-44system.The nm).Forthesereasons, theresults ofthissection shouldbe
first errorbar for each parameter is the statistical error, which used with care.
stemsfromthemeasuredspectroscopicandphotometricparame- The GROND instrument was conceived only for the
ters.Theseconderrorbaristhesystematicerrorarisingfromthe follow-up of gamma-ray bursts,and was not designed toal-
use of theoretical stellar models, and is given only for those pa- low filter changes for individual observing sequences. We
rameters whichhave adependence onstellartheory. Theresults were therefore unable to use filters with narrow pass-
fromAndersonetal.(2012)areincludedforcomparison.
bands covering specific wavelength ranges. We note that
the four optical bands of GROND were already used by
Thiswork(final) Andersonetal.(2012) deMooij et al. (2012) to investigate the atmosphere of
MA (M⊙) 0.917±0.077±0.051 0.951±0.034 GJ1214b, a 6.55M⊕ transiting planet. Here we try for the
RA (R⊙) 0.865±0.025±0.016 0.927+−00..006784 first time to use all the seven bands, exploiting the full po-
loggA (cgs) 4.526±0.018±0.008 4.481+−00..006587 tential of GROND.
ρA (ρ⊙) 1.414±0.058 1.19+−00..3222 Following the same strategy used by Southworth et al.
Mb (Mjup) 0.869±0.075±0.032 0.889±0.062 (2012b)andMancini et al.(2013),weproceeded asfollows.
Rb (Rjup) 1.002±0.033±0.018 1.14±0.11 ThetwoGRONDdatasetswerecombinedbyphaseandac-
gb (ms−2) 21.5±1.6 15.7+−33..40 cording to passband, and then fitted with all parameters
ρb (ρjup) 0.808±0.072±0.015 0.61+−00..2135 fixedtothefinalvaluesgiveninTable4,withtheexception
Teq (K) 1304±37 1343±64 of k. The LD coefficients were fixed to theoretical values.
Θ 0.0652±0.0048±0.0012 − The errors were estimated by a residual-permutation algo-
a(AU) 0.03445±0.00093±0.00063 0.03473±0.00041
Age(Gyr) 4.1−+56..90+−42..14 − ruinthcemrt(aSinotuythcwomormthon20t0o8a)l.lTdhatisasaeptps,roaallcohwirnegmuovsetsosmouarxcimesisoef
the accuracy of estimations of the fractional planetary ra-
tables7, a 0.875MJ planet with 50MEarth core at 0.045 AU diusrb=Rb/aasafunctionofwavelengthandwithrelative
errorbarsonly.TheresultsaredisplayedinFig.5,wherethe
fromtheSun(age3.16Gyr),is0.991RJup.Onthecontrary,
points show the data, the vertical bars represent the rela-
the expected radius for a core-free planet with the same
tive errors in the measurements and the horizontal bars in-
properties is 1.119RJup.
dicate the full widths at half maximum transmission of the
passbands used. The trasmission curves are also reported
3.4 Variation of planetary radius with wavelength forcompleteness. Asexpected,theuncertaintiesintheNIR
bands are larger, due to the larger scatter and systematic
Asan additionalpossibility fortheGRONDdata,wemade
features in thelight curves.
anattempttoinvestigatethepossiblevariationoftheradius
Inspection of Fig.5 shows that our measurements are
ofWASP-44bwithwavelength.Thisisquiteadifficulttask
unfortunatelynotsufficientlyaccuratetoclaim aclearvari-
because the relative faintness of the host star (V ∼ 12.9)
ation of r along the seven passbands. Using the plane-
b
makes this system less than ideal for optical photometric
tarysystem valuesreported inTable6,wecomputedaone-
studies, especially from the ground. Moreover, as already
dimensional model atmosphere of WASP-44b, using the
mentioned, our in-focus observing strategy has proved to
atmosphere code described in Fortney et al. (2005, 2008).
beill-suited toobtaininghigh-precision photometry,partic-
The fully non-gray model uses the chemical equilibrium
ularlyintheNIRbands.Finally,byusingbroad-bandfilters
abundances of Lodders & Fegley (2002) and the opacity
weareforcedtoaverageourmeasurementsoftheplanetra-
database described in Freedman et al. (2008). The atmo-
diusineachbandoveraquitelargerrangeofthewavelength
spheric pressure-temperature profile simulates planet-wide
(the best case in the i′ filter where its width is “only” 100
averageconditions.Wefurthermorecomputedthetransmis-
sion spectrum of the model using the methods described in
7 The tables, interpolated from the giant planet thermal evolu- Fortney et al. (2010).
tion models described in Fortneyetal. (2007), are available at Atopticalwavelengths,rb appearstobeslightly larger
http://www.ucolick.org/˜jfortney/models.htm in r′ and i′ than g′ and z′. This is as expected for a planet
Physical properties of WASP-44b 9
0.015
0.014
b
r
á á á á á á á
0.013
0.012
g¢ r i z J H K
500 1000 1500 2000
wavelength HnmL
Figure5.Variationofthefractionalplanetaryradiusrb=Rb/awithwavelength.ThepointsshownintheplotarefromtheMPG/ESO
2.2mtelescope.Theverticalbarsrepresenttheerrorsinthemeasurementsandthehorizontalbarsshowthefullwidthsathalfmaximum
transmissionofthepassbandsused.Thesolid,bluecontinuous lineisthecalculatedsyntheticspectrumbasedonatheoreticalmodelof
theatmosphereofWASP-44b.Redboxesindicatethepredictedvaluesforthismodelintegratedoverthepassbandsoftheobservations.
TransmissioncurvesoftheGRONDfiltersareshownatthebottom ofthefigure.
with an equilibrium temperature Teq ≈ 1300K, due to the 4 SUMMARY AND DISCUSSION
largerpredictedradiusaroundtheNaandKlines.Although
asimilar effectis seen inthemodel(Figure6),ourdataare Inthisworkwehavepresentedthefirstphotometricfollow-
not sufficiently precise to reject the default hypothesis that up of the transiting extrasolar planetary system WASP-44.
r is constant with wavelength. The radius of WASP-44b One transit was observed using WFC on the INT, and two
b
is in agreement with the theoretical model in the J band, transits were observed in seven passbands simultaneously
but is larger in the H and K bands. We found that the r using GROND on the MPG/ESO 2.2m telescope. Using
b
in r′ is 9.5% and 4.7% smaller than that for the H and K these new datasets plus another one taken from the liter-
band respectively,which correspond toa differencein units ature (Anderson et al. 2012), we have obtained improved
of atmospheric pressure scale height (H) of roughly 23H measurementsoftheorbitalephemeridesandphysicalprop-
and10H,respectively.Thefirstdifferenceisverylarge,and ertiesofthesystem.Inparticular, wefoundthattheradius
would involvean extremeopacity in H. ofWASP-44bissmallerthanpreviouslyfound,andisdiffer-
ent(at2σconfidencelevel)fromthattheoreticallyexpected
for a free-core planet (Fortney et al. 2007). This suggests
that WASP-44b is a “heavy element rich” planet, with the
heavyelements beinginadistinct coreormixed within the
H/Heenvelope. Sucharesult is important in order todraw
anaccurate mass–radius plot forTEPs, which provideskey
A more plausible alternative is that the NIR photome-
diagnostic for theoretical works that look to infer the bulk
tryisaffectedbysystematicsorcorrelated noise,whichwas
composition of the giant planets and distinguish them (in
notpossibletoeliminate.Thisisalsosuggestedbythepoor
some cases) from brown dwarfs.
SNR observed in the data, which is reflected in the higher
scatterofthepointsintheJ,H,K lightcurvesandthedif- AlthoughGRONDwasnotdesignedforfollow-upstud-
ferent shapes of the fit in the same band between the first iesofplanetarytransits,itisoneoftheveryfewimagingsys-
andthesecondobservedtransits(Figs.2and3).Wededuce tems worldwide able to perform simultaneous photometric
thatsystematicerrorsintheNIRdominatetheerrorbudget multi-band observations. The later fact makes GROND an
at these wavelengths. efficientandveryusefulinstrumenttodetecttransitanoma-
10 L. Mancini et al.
0.0138
Na
0.0136
K
0.0134
á á
á
á
b
r
0.0132
0.0130
0.0128
400 500 600 700 800 900
wavelength HnmL
Figure 6. As in Fig.5 but zoomed in on the optical wavelengths. In this range, the synthetic transmissionspectrum is dominated by
gaseous NaandK.
lies or to probe the atmosphere of TEPs. Indeed, atomic ACKNOWLEDGMENTS
and molecular absorption as well as scattering processes
Based on observations collected at the MPG/ESO 2.2m
may result in detectable radius variations as a function
Telescope located at ESO La Silla, Chile. Operations of
of wavelength (Fortney et al. 2007; Batygin et al. 2009).
this telescope are jointly performed by the Max Planck
deMooij et al. (2012) already used GROND in the case of
Gesellschaft and the European Southern Observatory.
GJ1214b,buttheyrestrictedtheiranalysisonlytotheopti-
GROND has been built by the high-energy group of MPE
calbands.Here,forthefirsttime,weusedallthesevenband
incollaboration withtheLSWTautenburgandESO,andis
ofthispowerfulinstrument,tosearchforvariationsofthera-
operating as a PI-instrument at the MPG/ESO 2.2m tele-
diusofWASP-44bwithwavelength.Wemeasuredtheplan-
scope. We thank David Anderson for supplying photomet-
etary radius in the seven GROND passbands, correspond-
ric data, and Timo Anguita and R´egis Lachaume for their
ingtoawavelengthcoverageof370–2440nm,andcompared
technical assistance during the observations. We thank the
themtoasyntheticspectrumbasedonanisothermalmodel
anonymousrefereefortheirusefulcriticismsandsuggestions
atmosphere in chemical equilibrium. The model reproduces
that helped us to improve the quality of the present paper.
theradiusvaluesintheoptical,inagreementwiththeequi-
Thereducedlightcurvespresentedinthisworkwillbemade
librium temperature of WASP-44b but, our data lack the
available at the CDS (http://cdsweb.u-strasbg.fr/). JS ac-
precision to rule out the possibility that the planetary ra-
knowledges financial support from STFC in the form of an
diusdoes not vary with wavelength. It does not predict the
AdvancedFellowship.
radius values found in the H and K bands, which differ
by roughly 23 and 10 atmospheric pressure scale heights to
those in the other bands. This phenomenon is most likely
due to the comparatively low quality of the NIR data. We REFERENCES
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